Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984027 | C2 | semidirect |
| 2. #22577641 | C2 | semidirect |
| 4. #22577229 | C2 | semidirect |
| 5. #22577207 | C2 | semidirect |
| 6. #22577204 | C2 | semidirect |
| 7. C2×SD32×C137 | C2 | semidirect |
| 39. C16×C137 | D4 | semidirect |
| 75. C137 | #2220 | semidirect |
| 77. C2×SD32 | D137 | semidirect |
| 115. C16 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984027 | 2 |
| #22577641 | 2 |
| #22577636 | 2 |
| #22577229 | 2 |
| #22577207 | 2 |
| #22577204 | 2 |
| C2×SD32×C137 | 2 |
| #2220 | 137 |